What is the Greatest Common Factor of 12900 and 12912?

Greatest common factor (GCF) of 12900 and 12912 is 12.

GCF(12900,12912) = 12

We will now calculate the prime factors of 12900 and 12912, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12900 and 12912.

How to find the GCF of 12900 and 12912?

We will first find the prime factorization of 12900 and 12912. After we will calculate the factors of 12900 and 12912 and find the biggest common factor number .

Step-1: Prime Factorization of 12900

Prime factors of 12900 are 2, 3, 5, 43. Prime factorization of 12900 in exponential form is:

12900 = 2² × 3¹ × 5² × 43¹

Step-2: Prime Factorization of 12912

Prime factors of 12912 are 2, 3, 269. Prime factorization of 12912 in exponential form is:

12912 = 2⁴ × 3¹ × 269¹

Step-3: Factors of 12900

List of positive integer factors of 12900 that divides 12900 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 43, 50, 60, 75, 86, 100, 129, 150, 172, 215, 258, 300, 430, 516, 645, 860, 1075, 1290, 2150, 2580, 3225, 4300, 6450

Step-4: Factors of 12912

List of positive integer factors of 12912 that divides 12900 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 269, 538, 807, 1076, 1614, 2152, 3228, 4304, 6456

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12900 and 12912. The biggest common factor number is the GCF number.
So the greatest common factor 12900 and 12912 is 12.

Also check out the Least Common Multiple of 12900 and 12912